MnO2 + HBr = H2O + Br2 + MnBr

MnO_2 manganese dioxide + HBr hydrogen bromide ⟶ H_2O water + Br_2 bromine + MnBr

Balance the chemical equation algebraically: MnO_2 + HBr ⟶ H_2O + Br_2 + MnBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 HBr ⟶ c_3 H_2O + c_4 Br_2 + c_5 MnBr Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, Br and H: Mn: | c_1 = c_5 O: | 2 c_1 = c_3 Br: | c_2 = 2 c_4 + c_5 H: | c_2 = 2 c_3 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 2 c_4 = 3/2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 8 c_3 = 4 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 MnO_2 + 8 HBr ⟶ 4 H_2O + 3 Br_2 + 2 MnBr

+ ⟶ + + MnBr

manganese dioxide + hydrogen bromide ⟶ water + bromine + MnBr

Construct the equilibrium constant, K, expression for: MnO_2 + HBr ⟶ H_2O + Br_2 + MnBr Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 2 MnO_2 + 8 HBr ⟶ 4 H_2O + 3 Br_2 + 2 MnBr Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i MnO_2 | 2 | -2 HBr | 8 | -8 H_2O | 4 | 4 Br_2 | 3 | 3 MnBr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnO_2 | 2 | -2 | ([MnO2])^(-2) HBr | 8 | -8 | ([HBr])^(-8) H_2O | 4 | 4 | ([H2O])^4 Br_2 | 3 | 3 | ([Br2])^3 MnBr | 2 | 2 | ([MnBr])^2 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([MnO2])^(-2) ([HBr])^(-8) ([H2O])^4 ([Br2])^3 ([MnBr])^2 = (([H2O])^4 ([Br2])^3 ([MnBr])^2)/(([MnO2])^2 ([HBr])^8)

Construct the rate of reaction expression for: MnO_2 + HBr ⟶ H_2O + Br_2 + MnBr Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 2 MnO_2 + 8 HBr ⟶ 4 H_2O + 3 Br_2 + 2 MnBr Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i MnO_2 | 2 | -2 HBr | 8 | -8 H_2O | 4 | 4 Br_2 | 3 | 3 MnBr | 2 | 2 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term MnO_2 | 2 | -2 | -1/2 (Δ[MnO2])/(Δt) HBr | 8 | -8 | -1/8 (Δ[HBr])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Br_2 | 3 | 3 | 1/3 (Δ[Br2])/(Δt) MnBr | 2 | 2 | 1/2 (Δ[MnBr])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/2 (Δ[MnO2])/(Δt) = -1/8 (Δ[HBr])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[Br2])/(Δt) = 1/2 (Δ[MnBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese dioxide | hydrogen bromide | water | bromine | MnBr formula | MnO_2 | HBr | H_2O | Br_2 | MnBr Hill formula | MnO_2 | BrH | H_2O | Br_2 | BrMn name | manganese dioxide | hydrogen bromide | water | bromine | IUPAC name | dioxomanganese | hydrogen bromide | water | molecular bromine |

| manganese dioxide | hydrogen bromide | water | bromine | MnBr molar mass | 86.936 g/mol | 80.912 g/mol | 18.015 g/mol | 159.81 g/mol | 134.84 g/mol phase | solid (at STP) | gas (at STP) | liquid (at STP) | liquid (at STP) | melting point | 535 °C | -86.8 °C | 0 °C | -7.2 °C | boiling point | | -66.38 °C | 99.9839 °C | 58.8 °C | density | 5.03 g/cm^3 | 0.003307 g/cm^3 (at 25 °C) | 1 g/cm^3 | 3.119 g/cm^3 | solubility in water | insoluble | miscible | | insoluble | surface tension | | 0.0271 N/m | 0.0728 N/m | 0.0409 N/m | dynamic viscosity | | 8.4×10^-4 Pa s (at -75 °C) | 8.9×10^-4 Pa s (at 25 °C) | 9.44×10^-4 Pa s (at 25 °C) | odor | | | odorless | |